Question

$3 \div 2 - x ^{2}$
I want the range step by step

Answer 1

●••••••••• Hello User ••••••••••●
《《 Here is your answer 》》
________________________

$let,\\ \\y=3 \div 2 - x ^{2}$

Domain of $x ^{2}$

x € R ....... Read as x below all real numbers.

The range $x ^{2}$

$0 \leqslant {x}^{2} \leqslant \infty$


Now, Multiplying -1 to each part of $- x ^{2}$ range.

$0 \times - 1 \geqslant - 1 \times {x}^{2} \geqslant - 1 \times \infty \\ \\ 0 \geqslant { - x}^{2} \geqslant - \infty$

Now, Adding $\frac{3}{2}$to each part of $- x ^{2}$ range.

$\frac{3}{2} + 0 \geqslant \frac{3}{2} + ( - { (x)}^{2} ) \geqslant \frac{3}{2} + - \infty \\ \\ \frac{3}{2} \geqslant \frac{3}{2} - {x}^{2} \geqslant \frac{3}{2} - \infty \\ \\ \frac{3}{2} \geqslant y \geqslant \frac{3}{2} - \infty$
y € [ - $\infty , \frac{3}{2}$ ]
____________________________
《《 Hope it may helpful to you 》》

○○○○○○○ @ajaman ○○○○○○○

●••••••• ☆ Brainly Star ☆ ••••••••●